Online Bin Stretching with Three Bins

Online Bin Stretching is a semi-online variant of bin packing in which the algorithm has to use the same number of bins as an optimal packing, but is allowed to slightly overpack the bins. The goal is to minimize the amount of overpacking, i.e., the maximum size packed into any bin. We give an algorithm for Online Bin Stretching with a stretching factor of $11/8 = 1.375$ for three bins. Additionally, we present a lower bound of $45/33 = 1.\overline{36}$ for Online Bin Stretching on three bins and a lower bound of $19/14$ for four and five bins that were discovered using a computer search.Comment: Preprint of a journal version. See version 2 for the conference paper. Conference paper split into two journal submissions; see arXiv:1601.0811

Semi-on-line multiprocessor scheduling with given total processing time

2004-2005 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

Radio Emission from a Young Supernova Remnant Interacting with an Interstellar Cloud: MHD Simulation with Relativistic Electrons

We present two-dimensional MHD simulations of the evolution of a young Type Ia supernova remnant during its interaction with an interstellar cloud of comparable size at impact. We include for the first time in such simulations explicit relativistic electron transport, including spectral information using a simple but effective scheme that follows their acceleration at shocks and subsequent transport. From this information we also model radio synchrotron emission, including spectra. The principal conclusions from these experiments are: 1) Independent of the cloud interaction, the SNR reverse shock can be an efficient site for particle acceleration in a young SNR. 2) At these early times the synchrotron spectral index due to electrons accelerated at the primary shocks should be close to 0.5 unless those shocks are modified by cosmic-ray pressures. However, interaction with the cloud generates regions of distinctly steeper spectra, which may complicate interpretation in terms of global dynamical models for SNR evolution. 3) The internal motions within the SNR become highly turbulent following the cloud interaction. 4) An initially uniform interstellar magnetic field is preferentially amplified along the magnetic equator of the SNR, primarily due to biased amplification by instabilities. Independent of the external field configuration, there is a net radial direction to this field inside the SNR. 5) Filamentary radio structures correlate well with magnetic filaments, while diffuse emission follows the electron distribution. 6) Interaction with the cloud enhances both the electron population and the radio emission.Comment: 29 pages of Latex generated text with 6 figures in gif format. Accepted for publication in the Astrophysical Journal. High resolution postscript figures can be obtained by anonymous ftp from ftp://ftp.msi.umn.edu/pub/users/twj/sn

The Crumpling Transition Revisited

The ``crumpling" transition, between rigid and crumpled surfaces, has been object of much discussion over the past years. The common lore is that such transition should be of second order. However, some lattice versions of the rigidity term on fixed connectivity surfaces seem to suggest that the transition is of higher order instead. While some models exhibit what appear to be lattice artifacts, others are really indistiguishable from models where second order transitions have been reported and yet appear to have third order transitions.Comment: Contribution to Lattice 92. 4 pages. espcrc2.sty file included. 6 figures upon request. UB-ECM-92/30 and UAB-FT-29

Mechanical forces regulate the interactions of fibronectin and collagen I in extracellular matrix

Despite the crucial role of extracellular matrix (ECM) in directing cell fate in healthy and diseased tissues--particularly in development, wound healing, tissue regeneration and cancer--the mechanisms that direct the assembly and regulate hierarchical architectures of ECM are poorly understood. Collagen I matrix assembly in vivo requires active fibronectin (Fn) fibrillogenesis by cells. Here we exploit Fn-FRET probes as mechanical strain sensors and demonstrate that collagen I fibres preferentially co-localize with more-relaxed Fn fibrils in the ECM of fibroblasts in cell culture. Fibre stretch-assay studies reveal that collagen I's Fn-binding domain is responsible for the mechano-regulated interaction. Furthermore, we show that Fn-collagen interactions are reciprocal: relaxed Fn fibrils act as multivalent templates for collagen assembly, but once assembled, collagen fibres shield Fn fibres from being stretched by cellular traction forces. Thus, in addition to the well-recognized, force-regulated, cell-matrix interactions, forces also tune the interactions between different structural ECM components.233157 - European Research Council; PN2 EY016586 - NEI NIH HH